This disclosure relates to phase-shifting interferometry.
Interferometric optical techniques are widely used to measure optical thickness, flatness, and other geometric and refractive index properties of precision optical components such as glass substrates used in lithographic photomasks.
For example, one can use an interferometer to combine a measurement wavefront reflected from a measurement surface with a reference wavefront reflected from a reference surface to form an optical interference pattern. Spatial variations in the intensity profile of the optical interference pattern correspond to phase differences between the combined measurement and reference wavefronts caused by, for example, variations in the profile of the measurement surface relative to the reference surface. Phase-shifting interferometry (PSI) can be used to accurately determine the phase differences and the corresponding profile of the measurement surface.
In linear PSI, a time dependent phase shift which varies linearly in time is introduced between the reference and measurement wavefronts. The optical interference pattern is recorded for each of multiple phase-shifts between the reference and measurement wavefronts to produce a series of optical interference patterns that span a full cycle of optical interference (e.g., from constructive, to destructive, and back to constructive interference). The optical interference patterns define a series of intensity values for each spatial location of the pattern, wherein each series of intensity values has a sinusoidal dependence on the phase-shifts with a phase difference equal to the phase difference between the combined measurement and reference wavefronts for that spatial location. Using numerical techniques known in the art, the phase difference for each spatial location is extracted from the sinusoidal dependence of the intensity values. These phase differences can be used to determine information about the test surface including, for example, a profile of the measurement surface relative the reference surface. Such numerical techniques are referred to as linear phase-shifting algorithms.
The phase-shifts in PSI can, for example, be produced by a modulating means which changes the optical path length from the measurement surface to the interferometer relative to the optical path length from the reference surface to the interferometer. For example, the reference surface can be moved relative to the measurement surface or a modulator may be placed in one of the beam paths. Alternatively, the phase-shifts can be introduced for a constant, non-zero optical path difference by changing the wavelength of the measurement and reference wavefronts. The latter application is known as wavelength tuning PSI and is described, e.g., in U.S. Pat. No. 4,594,003 to G. E. Sommargren. The ability of certain types of modulating means (e.g. piezoelectric transducers, wavelength tunable lasers, etc) to produce a linear phase shifts may be limited, due to, for example, bandwidth limitations.
The interference signal in a PSI system is typically detected by a conventional camera system, converted to electronic data, and read out to a computer for analysis. In such applications, the optical interference signal is imaged onto an array of pixels. Charge accumulates at each pixel at a rate that depends on the intensity of the incident light. The charge value at each pixel is then read out, or transferred to a data processing unit.